few_shots: Example:
Problem/activity:
Task
Materials
One 10-frame per pair of students (see example below)
[IMG]
Counters, 10 per pair of students
Decks of number cards 0-5 (with 4 of each number) or two 0-5 dice
Setup
This activity is done in pairs. The students sit side by side with 10-frame and deck of cards or dice. If they have cards, the cards are shuffled and placed face down in front of them.
Action
Player 1 flips a card or rolls the die. They place that many counters on the 10-frame. Player 2 flips a card or rolls the die. They place that many more counters on the 10-frame next to the counters already on the ten frame. The students count the total together.
A recording sheet can be added when the students have been introduced to equations and number sentences. For those students who can handle higher numbers, a deck of 0-10 cards and two 10-frames can be used.
This game can also be played alone.


Mathematical concept/skill options: 
A. Write and interpret numerical expressions.
B. Generate and analyze patterns.
C. Analyze patterns and relationships.
D. Use properties of operations to generate equivalent expressions.
E. Use the four operations with whole numbers to solve problems.
F. Work with radicals and integer exponents.
G. Solve systems of equations.
H. Represent and solve problems involving multiplication and division.
I. Perform arithmetic operations on polynomials.
J. Understand the relationship between zeros and factors of polynomials.
K. Understand properties of multiplication and the relationship between multiplication and division.
L. Solve real-life and mathematical problems using numerical and algebraic expressions and equations.
M. Solve problems involving the four operations, and identify and explain patterns in arithmetic.
N. Use polynomial identities to solve problems.
O. Apply and extend previous understandings of arithmetic to algebraic expressions.
P. Rewrite rational expressions.
Q. Interpret the structure of expressions.
R. Add and subtract within 20.
S. Analyze and solve linear equations and pairs of simultaneous linear equations.
T. Represent and analyze quantitative relationships between dependent and independent variables.
U. Solve equations and inequalities in one variable.
V. Create equations that describe numbers or relationships
W. Reason about and solve one-variable equations and inequalities.
X. Represent and solve equations and inequalities graphically.
Y. Understand solving equations as a process of reasoning and explain the reasoning.
Z. Understand and apply properties of operations and the relationship between addition and subtraction.
AA. Gain familiarity with factors and multiples.
AB. Understand addition as putting together and adding to, and understand subtraction as taking apart and taking from.
AC. Work with addition and subtraction equations.
AD. Multiply and divide within 100.
AE. Work with equal groups of objects to gain foundations for multiplication.
AF. Represent and solve problems involving addition and subtraction.
AG. Write expressions in equivalent forms to solve problems.
AH. Understand the connections between proportional relationships, lines, and linear equations.


Thought: This task teaches students to understand addition as putting together counters, or adding to already placed counters.
Answer: AB

Now, assign the following problem or activity to one or more relevant mathematical concepts/skills it teaches.
shot_info: im_task_001477

K
options: Calculate expected values and use them to solve problems.

Use probability to evaluate outcomes of decisions.

Summarize, represent, and interpret data on a single count or measurement variable.

Summarize, represent, and interpret data on two categorical and quantitative variables.

Develop understanding of statistical variability.

Understand independence and conditional probability and use them to interpret data.

Use random sampling to draw inferences about a population.

Use the rules of probability to compute probabilities of compound events in a uniform probability model.

Investigate patterns of association in bivariate data.

Draw informal comparative inferences about two populations.

Summarize and describe distributions.

Make inferences and justify conclusions from sample surveys, experiments, and observational studies.

Investigate chance processes and develop, use, and evaluate probability models.

Understand and evaluate random processes underlying statistical experiments.

Interpret linear models.
problem_activity: Activity
Now that students are more familiar with two-way tables showing relative frequency, they are ready to create their own segmented bar graphs. In this activity, students create two segmented bar graphs based on the same two-way table by considering percentages of the rows and columns separately. After creating the segmented bar graphs, they are analyzed to determine if there is an association present in the data.
Launch
Arrange students in groups of 2. After a brief introduction, give 5–10 minutes of quiet work time. Ask students to compare their answers with their partner and try to resolve any differences. Finish with a whole-class discussion.
Display the two-way table from the previous lesson's cool-down activity containing the data collected about the class's playing sports and musical instruments. If the data is unavailable, the data from this lesson's warm-up can be used.
Tell students they should work with their partners to each work on one of the graphs. One student should work on problems 1 and 2 while their partner should work on 3 and 4. After they have completed their graphs, they should work together to understand their partners graphs and complete the last problem together.
Action and Expression: Internalize Executive Functions.
Chunk this task into more manageable parts to support students who benefit from support with organization and problem solving. For example, present one question at a time. Some students may benefit from a checklist on how to create a segmented bar graph.
Supports accessibility for: Organization; Attention
Student Facing
Your teacher will give you a two-way table with information about the number of people in your class who play sports or musical instruments.
Complete this table to make a two-way table for the data from earlier. The table will show relative frequencies
by row
.
|                     | plays instrument | does not play instrument | row total |
|---------------------|------------------|--------------------------|-----------|
|     plays sport     |                  |                          |           |
| does not play sport |                  |                          |           |
Make a segmented bar graph for the table. Use one bar of the graph for each row of the table.
[IMG]
Complete the table to make a two-way table for the data from earlier. The table will show relative frequencies
by column
.
|                     | plays instrument | does not play instrument |
|---------------------|------------------|--------------------------|
|     plays sport     |                  |                          |
| does not play sport |                  |                          |
|    column total     |                  |                          |
Using the values in the table, make a segmented bar graph. Use one bar of the graph for each column of the table.
[IMG]
Based on the two-way tables and segmented bar graphs, do you think there is an association between playing a sport and playing a musical instrument? Explain how you know.
Student Response
Teachers with a valid work email address can
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Anticipated Misconceptions
Students may draw the segmented bar graph incorrectly. Most likely, they will accidentally graph frequency instead of relative frequency. They may also graph relative frequencies, but without stacking them. Both segmented bars should go from 0 to 100.
Activity Synthesis
To clarify how to create and interpret segmented bar graphs, ask:
“What different information can be seen by the two segmented bar graphs?”
“Why are the numbers in the top left box in the two tables different? What do they mean?” (In the first table it represents the percentage who also play musical instruments out of all the people who play sports. In the second table it represents the percentage of people who also play sports out of all the people who play musical instruments.)
“Is there an association between the two variables? Explain or show your reasoning.” (The answer will depend on class data, but the reasoning should include an analysis of the relative frequencies within categories. There is an association if the percentages within one category are very different from the percentages in another category.)
If there is an association, ask what the segmented bar graphs would look like if there was no association. If there is not an association, ask what the segmented bar graphs would look like if there was one.
Writing, Speaking: MLR1 Stronger and Clearer Each Time.
Use this routine to give students a structured opportunity to revise and refine their response to the last question. Ask each student to meet with 2–3 other partners in a row for feedback. Provide students with prompts for feedback that will help them strengthen their ideas and clarify their language (e.g., “Why do you think there is a (positive/negative) association?”, “How do the relative frequencies help to answer this question?”, “How could you say that another way?”, etc.). Students can borrow ideas and language from each partner to strengthen the final product. They can return to the first partner and revise and refine their initial response.
Design Principle(s): Optimize output (for explanation)


correct_option_index: 8